In DE 43 43 429 C2, a clamping device with mechanical damping is disclosed, which is provided for a traction mechanism drive, with the device comprising a clamping arm, which carries a tension roller on one end, which is rotatably mounted in a housing via a shaft connected in a rotationally fixed manner on its other end, and which is elastically supported on the housing by means of a torsion and compression spring, wherein the free end of the shaft is connected in a rotationally fixed manner to a friction disk and a friction lining is arranged between the friction disk and an axial abutment surface of the housing. The abutment surface of the housing has a plurality of sharp-edged projections, which extend in the axial direction and which dig into the friction lining. Therefore, the friction lining is connected rigidly to the abutment surface of the housing, while the damping motion takes place between the friction lining and the friction disk. This solution requires a relatively soft friction lining, which is less stable. In addition, strong heating occurs on the friction lining, because the steel friction disk dissipates the friction heat only poorly. The high temperatures also cause increased wear on the friction lining and reduced damping capacity.